In a turbomachine such as an aeronautical gas turbine engine, the shafts connecting the various compressor and turbine disks are principal component parts revolving at high speed and capable of withstanding high loadings while at the same time needing to remain relatively light in weight. Their manufacture involves boring a longitudinal cavity in the forging, the exterior surface of which has already been machined. After this boring operation, the internal dimensions of the shaft need to be checked in order in particular to be able to make any corrections that might be needed in order to confine the wall thickness to a certain tolerance band.